Free Printable Simplifying Rational Expressions

1.

Simplify the rational expression and identify the excluded values.
$\frac{xy^3}{x^2y}$

a)

$\frac{xy}{x};\ x\ne0$

b)

$\frac{y^2}{x};x\ne0$

c)

$xy^2;\ x\ne0$

d)

$\frac{y^2}{x};x\ne0;y\ne0$

2.

$\frac{x^2y}{xy}$ Simplify the rational expression and state the excluded values.

a)

$\frac{x}{y};\ x\ne0;y\ne0$

b)

$\frac{x}{y};y\ne0$

c)

$x;x\ne0;y\ne0$

d)

$x^2;y\ne0$

3.

$\frac{5ab^3}{10ab^4}$ Simplify the rational expression and state the excluded values.

a)

$\frac{1}{2b};a\ne0;b\ne0$

b)

$\frac{b}{2};b\ne0$

c)

$\frac{a}{2b};a\ne0;b\ne0$

d)

$\frac{a}{2};none$

4.

$\frac{12a^2b}{4a^3b}$ Simplify the rational expression and state the excluded values.

a)

$\frac{3b}{a};a\ne0$

b)

$\frac{3b}{a};a\ne0;b\ne0$

c)

$\frac{3}{a};a\ne0$

d)

$\frac{3}{a};a\ne0;b\ne0$

5.

$\frac{15xy^3z}{25x^2y^2z}$ Simplify the rational expression and state the excluded values.

a)

$\frac{y}{5x};x\ne0;y\ne0$

b)

$\frac{3yz}{5x};x\ne0$

c)

$\frac{3y}{5x};x\ne0;y\ne0;z\ne0$

d)

$\frac{3yz}{x};x\ne0;y\ne0;z\ne0$

6.

$\frac{8ab^2c^3}{36a^2bc^2}$ Simplify the rational expression and state the excluded values.

a)

$\frac{bc}{4a};a\ne0$

b)

$\frac{2bc}{9a};a\ne0;b\ne0;c\ne0$

c)

$\frac{2c}{6a};a\ne0$

d)

$\frac{2c}{9ab};a\ne0;b\ne0;c\ne0$

7.

$\frac{18\left(x-4\right)}{48\left(x-4\right)}$ Simplify the rational expression and state the excluded values.

a)

$\frac{18}{x-4};x\ne\left\{0,4\right\}$

b)

$\frac{3}{x-4};x\ne\left\{3,4\right\}$

c)

$\frac{3}{8};x\ne\left\{0,-4\right\}$

d)

$\frac{3}{8};x\ne4$

8.

$\frac{48\left(x+3\right)}{60\left(x+3\right)}$ Simplify the rational expression and state the excluded values.

a)

$\frac{12}{15};x\ne3$

b)

$\frac{12}{15};x\ne-3$

c)

$\frac{4}{5};x\ne3$

d)

$\frac{4}{5};x\ne-3$

9.

$\frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x-1\right)}$ Simplify the rational expression and state the excluded values.

a)

$1;x\ne\left\{1,2\right\}$

b)

$\frac{x+1}{x-1};x\ne1$

c)

$\frac{1}{x-1};x\ne\left\{-1.-2\right\}$

d)

$\frac{x+1}{x-1};x\ne\left\{1,2\right\}$

10.

$\frac{\left(x+5\right)\left(x-3\right)}{\left(x-4\right)\left(x-3\right)}$ Simplify the rational expression and state the excluded values.

a)

$\frac{x+5}{x-4};x\ne4$

b)

$\frac{x+5}{x-4};x\ne-4$

c)

$\frac{x+5}{x-4};x\ne\left\{-4,-3\right\}$

d)

$\frac{x+5}{x-4};x\ne\left\{3,4\right\}$

11.

$\frac{x-2}{x^2-4}$ Simplify the rational expression and state the excluded values.

a)

$\frac{1}{x+2};x\ne2$

b)

$\frac{1}{x+2};x\ne\left\{-2,2\right\}$

c)

$\frac{1}{x-2};x\ne4$

d)

$\frac{1}{x+2};x\ne4$

12.

$\frac{a+3}{a^2-9}$ Simplify the rational expression and state the excluded values.

a)

$\frac{a+3}{a-3};a\ne9$

b)

$\frac{1}{a-3};a\ne\left\{3,-3\right\}$

c)

$\frac{1}{a+3};a\ne\left\{-3,3\right\}$

d)

$\frac{-1}{a-3};a\ne\left\{-3,3\right\}$

13.

$\frac{x-4}{16-x^2}$ Simplify the rational expression and state the excluded values.

a)

$\frac{-1}{4-x};x\ne16$

b)

$\frac{-1}{x+4};x\ne\left\{-4,4\right\}$

c)

$\frac{x-4}{\left(4-x\right)\left(4+x\right)};x\ne\left\{-4,4\right\}$

d)

$\frac{x-4}{4+x};x\ne\left\{-4,4\right\}$

14.

$\frac{x^3-8}{2-x}$ Simplify the rational expression and state the excluded values.

a)

$x+2;x\ne2$

b)

$x^2+2x+4;x\ne2$

c)

$\frac{x^2+4}{2-x};x\ne2$

d)

$-x^2-2x-4;x\ne2$

15.

Simplify the rational expression and state the excluded values.
$\frac{20-30x}{3x^2-2x}$

a)

$\frac{10\left(2-3x\right)}{x\left(3x-2\right)};x\ne-\frac{2}{3}$

b)

$\frac{10}{x};x\ne\frac{2}{3}$

c)

$\frac{-10}{x};x\ne\left\{\frac{2}{3},0\right\}$

d)

$\frac{10}{-x};x\ne0$

16.

$\frac{15-3x}{2x^2-10x}$ Simplify the rational expression and state the excluded values.

a)

$\frac{-3}{2x};x\ne\left\{-5,0\right\}$

b)

$\frac{3}{2x};x\ne\left\{-5,0\right\}$

c)

$\frac{-3}{2x};x\ne\left\{5,0\right\}$

d)

$\frac{3\left(5-x\right)}{2x\left(x-5\right)};\ x\ne\left\{0,5\right\}$

17.

$\frac{x^2-1}{2x^2+x-3}$ Simplify the rational expression and state the excluded values.

a)

$\frac{\left(x+1\right)}{\left(2x+3\right)};x\ne\left\{-\frac{3}{2},1\right\}$

b)

$\frac{1}{2x+3};x\ne\left\{-\frac{3}{2},1\right\}$

c)

$\frac{x-1}{2x+3};x\ne\left\{-\frac{2}{3},1\right\}$

d)

$\frac{1}{2x+3};x\ne-\frac{2}{3}$

18.

$\frac{x^2-4x+4}{x^2-4}$ Simplify the rational expression and state the excluded values.

a)

$x+4;x\ne4$

b)

$\frac{\left(x-2\right)}{\left(x+2\right)};x\ne\left\{-2,2\right\}$

c)

$\frac{x-2}{x+2};x\ne\left\{0,-2\right\}$

d)

$\frac{x+1}{x};x\ne\left\{0,4\right\}$

19.

$\frac{x^2-7x+6}{x^2+3x-54}$ Simplify the rational expression and state the excluded values.

a)

$\frac{x-6}{x-3};x\ne\left\{3,6,9\right\}$

b)

$\frac{x+6}{x+9};x\ne\left\{6,-9\right\}$

c)

$\frac{x+1}{x-9};x\ne\left\{9,-6\right\}$

d)

$\frac{x-1}{x+9};x\ne\left\{6,-9\right\}$

20.

$\frac{2x^2+x-1}{x^2-x-2}$ Simplify the rational expression and state the excluded values.

a)

$\frac{2x-1}{x+2};x\ne\left\{-2,-1\right\}$

b)

$\frac{2x-1}{x-2};x\ne\left\{-1,2\right\}$

c)

$\frac{2x-1}{x-2};x\ne\left\{\frac{1}{2},2\right\}$

d)

$\frac{2x+1}{x-2};x\ne\left\{2,-1\right\}$

Simplifying Rational Expressions

Total questions: 20

Worksheet time: 17mins

Similar Resources on Wayground